International Journal Of Computational Engineering Research (Ijceronline.Com) Vol. 2 Issue.5 Issn 2250-3005(online) September| 2012 Page 1502 Design of Classifier for Detecting Image Tampering Using Gradient Based Image Reconstruction Technique Sonal Sharma, Preeti Tuli Abstract Image tampering detection is a significant multimedia forensics topic which involves, assessing the authenticity or not of a digital image. Information integrity is fundamental in a trial but it is clear that the advent of digital pictures and relative ease of digital image processing makes today this authenticity uncertain. In this paper this issue is investigated and a framework for digital image forensics is presented, individuating if the tampering has taken place. Based on the assumptions that some processing must be done on the image before it is tampered, and an expected distortion after processing an image, we design a classifier that discriminates between original and tampered images. We propose a novel methodology based on gradient based image reconstruction to classify images as original or tampered. This methodology has its application in a context where the source image is available (e.g. the forensic analyst has to check a suspect dataset which contains both the source and the destination image). Index Terms — Gradient, Poisson equation, Region of interest (ROI), Digital image forensics, Authenticity verification, Image reconstruction from gradients. 1 INTRODUCTION N today’s digital age, the creation and manipulation of digital images is made simple by digital processing tools that are e asily and widely available. As a consequence, we can no longer take the authenticity of images for granted especially when it comes to legal photographic evidence. Image forensics, in this context, is concerned with determining the source and potential authenticity of an image. Although digital watermarks have been proposed as a tool to provide authenticity to images, it is a fact that the overwhelming majority of images that are captured today do not contain a digital watermark. And this situation is likely to con- tinue for the foreseeable future. Hence in the absence of widespread adoption of digital watermarks, there is a strong need for developing techniques that can help us make statements about the origin, veracity and authenticity of digital images. In this paper we focus on the problem of reliably discriminating between “tampered” images (images which are altered in order to deceive people) from untampered original ones. The basic idea behind our approach is that a tammpered image (or the least parts of it) would have undergone some image processing. Hence, we design a classifier that can distinguish between images that have and have not been processed. We apply it to a suspicious image of a target image and classify the suspicious image as tam- pered or untampered. The rest of this paper is organized as follows: In Section 2we present a method to verify the authenticity of images that is used in the classifier we design for image forensics, i.e. we formulate the problem and present solution methodol- ogy. Statistical performance results are given in Section 3, with conclusions drawn in section 4. 2 PROBLEM FORMULATION AND SOLUTION METHODOLOGY The problem of fraud detection has been faced by proposing different approaches each of these based on the same concept: a forgery introduces a correlation between the original image and the tampered one. Several methods search for this dependence by analyzing the image and then applying a feature extraction process. In [1] the direct approach proposed by Fridrich et al. comprises of performing an exhaustive search by comparing the image to every cyclic – shifted versions of it, which requires (MN 2 ) steps for an image sized M by N. This computationally expensive search does not work where the copied region has undergone modifications. In [2] A.N. Myma et al. presented an approach of first applying wavelet transform to the input image to yield a reduced dimension representation, then exhaustive search is performed to identify similar blocks in the image by mapping them to log polar co-ordinates and using phase correlation as the similarity criterion. But the performance relies on the location of copy- move regions. In [3] Weihai Li et al. utilized the mismatch of information of block artifact grid as clue of copy paste forgery. A DCT grid is the horizontal lines and the vertical lines that partition an image into blocks and a block artifact grid (BAG) is the grid embedded in an image where block artifact appears. The DCT grid and BAG match together in untampered images. But if the copied area is from the other different image it cannot be detected by the method, also the complexity of algorithm is high. In [4] Bayram et al. proposed Fourier – Mellin transform (FMT). But the algorithm works for the case of only slight rotation. In [5] Xu Bo et al. proposed a method in which Speed up Robust features (SURF) key points are extracted and their descriptors are matched within each other with a threshold value. This method fails to automatically locate the tampered I
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International Journal Of Computational Engineering Research (Ijceronline.Com) Vol. 2 Issue.5
Issn 2250-3005(online) September| 2012 Page 1502
Design of Classifier for Detecting Image Tampering Using Gradient
Based Image Reconstruction Technique
Sonal Sharma, Preeti Tuli
Abstract
Image tampering detection is a significant multimedia forensics topic which involves, assessing the authenticity or not of a
digital image. Information integrity is fundamental in a trial but it is clear that the advent of digital pictures and relative
ease of digital image processing makes today this authenticity uncertain. In this paper this issue is investigated and a
framework for digital image forensics is presented, individuating if the tampering has taken place. Based on the
assumptions that some processing must be done on the image before it is tampered, and an expected distortion after
processing an image, we design a classifier that discriminates between original and tampered images. We propose a novel
methodology based on gradient based image reconstruction to classify images as original or tampered. This methodology
has its application in a context where the source image is available (e.g. the forensic analyst has to check a suspect dataset
which contains both the source and the destination image).
Index Terms — Gradient, Poisson equation, Region of interest (ROI), Digital image forensics, Authenticity verification,
Image reconstruction from gradients.
1 INTRODUCTION
N today’s digital age, the creation and manipulation of digital images is made simple by digital processing tools that are easily
and widely available. As a consequence, we can no longer take the authenticity of images for granted especially when it comes to
legal photographic evidence. Image forensics, in this context, is concerned with determining the source and potential authenticity
of an image. Although digital watermarks have been proposed as a tool to provide authenticity to images, it is a fact that the
overwhelming majority of images that are captured today do not contain a digital watermark. And this situation is likely to con-
tinue for the foreseeable future. Hence in the absence of widespread adoption of digital watermarks, there is a strong need for
developing techniques that can help us make statements about the origin, veracity and authenticity of digital images.
In this paper we focus on the problem of reliably discriminating between “tampered” images (images which are altered in order
to deceive people) from untampered original ones. The basic idea behind our approach is that a tammpered image (or the least
parts of it) would have undergone some image processing. Hence, we design a classifier that can distinguish between images that
have and have not been processed. We apply it to a suspicious image of a target image and classify the suspicious image as tam-
pered or untampered. The rest of this paper is organized as follows: In Section 2we present a method to verify the authenticity of
images that is used in the classifier we design for image forensics, i.e. we formulate the problem and present solution methodol-
ogy. Statistical performance results are given in Section 3, with conclusions drawn in section 4.
2 PROBLEM FORMULATION AND SOLUTION METHODOLOGY The problem of fraud detection has been faced by proposing different approaches each of these based on the same concept: a
forgery introduces a correlation between the original image and the tampered one. Several methods search for this dependence
by analyzing the image and then applying a feature extraction process. In [1] the direct approach proposed by Fridrich et al.
comprises of performing an exhaustive search by comparing the image to every cyclic – shifted versions of it, which requires
(MN2) steps for an image sized M by N. This computationally expensive search does not work where the copied region has
undergone modifications. In [2] A.N. Myma et al. presented an approach of first applying wavelet transform to the input image
to yield a reduced dimension representation, then exhaustive search is performed to identify similar blocks in the image by
mapping them to log polar co-ordinates and using phase correlation as the similarity criterion. But the performance relies on the
location of copy- move regions. In [3] Weihai Li et al. utilized the mismatch of information of block artifact grid as clue of copy
paste forgery. A DCT grid is the horizontal lines and the vertical lines that partition an image into blocks and a block artifact grid
(BAG) is the grid embedded in an image where block artifact appears. The DCT grid and BAG match together in untampered
images. But if the copied area is from the other different image it cannot be detected by the method, also the complexity of
algorithm is high. In [4] Bayram et al. proposed Fourier – Mellin transform (FMT). But the algorithm works for the case of only
slight rotation. In [5] Xu Bo et al. proposed a method in which Speed up Robust features (SURF) key points are extracted and
their descriptors are matched within each other with a threshold value. This method fails to automatically locate the tampered
I
International Journal Of Computational Engineering Research (Ijceronline.Com) Vol. X Issue. X
Issn 2250-3005(online) September| 2012 Page 1503
region and its boundary. None of these approaches [1, 2, 3, 4, and 5] conducts authentication verification using gradient maps in the image reconstruction.
The approach presented in this paper verifies the authentication in two phases modeling phase and simulation phase. In modeling
phase the image is reconstructed from the image gradients by solving a poisson equation and in the simulation phase absolute
difference method and histogram matching criterion between the original and test image is used. The solution methodology is
discussed in the subsequent paragraphs.
2.1 Image Reconstruction
In the year 1993 Luc Vincent [6] carried out the work in morphological grayscale reconstruction. In 2004 Di Zang and G.
Sommer [7] carried out phase based image reconstruction in the monogenic scale space. In 2005 S. Leng et al. [8] presented fan-
beam image reconstruction algorithm to reconstruct an image via filtering a back projection image of differentiated projection
data. In 2008 A. L. Kesidis and N. Papamarkos [9] presented a new method for the exact image reconstruction from projections.
The original image is projected into several view angles and the projection samples are stored in an accumulator array. In 2011 P.
Weinzaepfel et al [10] proposed another novel approach which consists using an off-the-shelf image database to find patches
visually similar to each region of interest of the unknown input image.
The approach presented in this paper is gradient based image reconstruction by solving poisson equation. The details of the
method are described as under:
2.1.1 Gradient Based Image Reconstruction:
As already stated in our previous work [11] image reconstruction from gradient fields is a very active research area. The gradi-
ent-based image processing techniques and the poisson equation solving techniques have been addressed in several related areas
such as high dynamic range compression [12], Poisson image editing [13], image fusion for context enhancement [14], interac-
tive photomontage [15], Poisson image matting [16] and photography artifacts removal [17]. A new criterion is developed, where
the image is reconstructed from its gradients by solving a poisson equation and hence used for authenticity verification [11].
In 2D, a modified gradient vector field,
G’ = [G’x, G’y]
(1)may not be integrable.
Let I’ denote the image reconstructed from G’, we employ one of the direct methods recently proposed in [12] to minimize,
|| ∇ I’ – G||
(2)so that,
G ≈ ∇ I’
(3)By introducing a Laplacian and a divergence operator, I’ can be obtained by solving the Poisson differential equation [18, 19]
∇ 2 I’ = div([G’x,G’y])
Since both the Laplacian and div are linear operators, approximating those using standard finite differences yields a large system
of linear equations. The full multigrid method [20] is used to solve the Laplacian equation with Gaussian-Seidel smoothing
iterations. For solving the poisson equation more efficiently, an alternative is to use a rapid poisson solver, which uses a sine
transform based on the method [18] to invert the laplacian operator. Therefore, the rapid poisson solver is employed in our
implementation. The image is zero-padded on all sides to reconstruct the image.
2.1.2 Poisson Solvers:
A Poisson solver produces the image whose gradients are closest to the input manipulated gradient domain image in a least
squares sense, thereby doing a kind of inverse gradient transform. Note that if the input were a gradient domain image whose
gradients had not been manipulated, the inverse gradient transformation would have an exact solution, and the poisson equation
would give a perfect reconstruction of the image. Both the FFT-based solver and the poisson solver using zero Dirichlet bounda-
ry condition work successfully in obtaining an inverse gradient transformation in the sense that they give a perfect reconstruction
of the image when the input gradient domain image is not manipulated. This section details the poisson solver which has been
used in the present research work.
In this section, we describe the standard gradient integration problem and its poisson solution and then expand this result to in-
clude a data function term. The problem of computing a function f (x,y) whose gradient ∇f (x,y) is as close as possible to a given
gradient field g (x,y) is commonly solved by minimizing the following objective:
∫ ∫ || ∇f – g ||2 dx dy.
Note that g is a vector-valued function that is generally not a gradient derived from another function. (If g were derived from
another function, then the optimal f would be that other function, up to an unknown constant offset.)
It is well-known that, by applying the Euler-Lagrange equation, the optimal f satisfies the following Poisson equation:
∇2 f = ∇· g,
International Journal Of Computational Engineering Research (Ijceronline.Com) Vol. X Issue. X
Issn 2250-3005(online) September| 2012 Page 1504
(6) which can be expanded as fxx + fyy = gxx + gy
y , where g = (g
x, g
y). Subscripts in x and y correspond to partial derivatives with
respect to those variables. We have superscripted gx and g
y to denote the elements of g rather than subscript them, which would
incorrectly suggest they are partial derivatives of the same function.We now expand the objective beyond the standard formula-
tion. In particular, we additionally require f(x, y) to be as close as possible to some data function u(x, y). The objective function
to minimize now becomes:
∫ ∫ λd (f − u)2 + ||∇f – g||
2 dx dy,
(7)Where, λd is a constant that controls the trade-off between the fidelity of f to the data function versus the input gradient field.
To solve for the function f that minimizes this integral, we first isolate the integrand:
L = λd (f − u)2 + ||∇f – g||
2 = λd (f − u)
2 + (fx − g
x)
2 + (fy − g
y)
2
(8)The function f that minimizes this integral satisfies the Euler-Lagrange equation: